Whisk together the flour and salt and place the mixture on a dry, clean surface.
Create a hole in the center of the flour and salt mixture and place the eggs and egg yolks. Using a fork, gradually incorporate small amounts of the dry ingredients into the egg mixture, moving in a circle around the center. Work until the dry ingredients have been fully incorporated. If the dough crumbles or does not remain together, add 1 tbsp of water or olive oil and knead until incorporated. (This step can also be performed in a stand mixer by first using the flat paddle attachment, followed by the dough hook attachment.)
Working on a flat surface, knead the dough for one minute. Then, roll the dough to about one-inch thickness, cover it with plastic wrap, and let it rest for 45-60 minutes.
Divide the dough into manageable pieces, such as halves or thirds. Using one piece at a time, roll the dough to about ½-inch thickness and let it rest for 5-10 minutes.
Using a pasta roller, feed the dough through the machine until the desired thickness is achieved. If using a Kitchenaid past making attachment, begin at setting 2. Roll the dough once, then fold the dough by thirds, before rolling it again at this setting. Increase to setting 3 and pass the dough through the machine again. Repeat this step, increasing to settings 4, 5, and 6.
At this stage, the dough can be cut or used to make ravioli or any other pasta dish.